The invention relates to a method and a device for welding cylindrical elements headwise to one another. In welding cylindrical elements to one another care has to be taken for the parts to be welded to accurately engage one another with aligned heads. It may also occur that the elements do not exhibit the desired circumferential shape, for example, a circular circumference, and during the welding process this has to be corrected. After welding the continuity of the resulting cylindrical wall should be disturbed as little as possible, while the axes of the welded elements should coincide as accurately as possible.